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Simplifying -4n2 + 6n + -16 = 5n2 Reorder the terms: -16 + 6n + -4n2 = 5n2 Solving -16 + 6n + -4n2 = 5n2 Solving for variable 'n'. Combine like terms: -4n2 + -5n2 = -9n2 -16 + 6n + -9n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 -16 + 6n + -9n2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 1.777777778 + -0.6666666667n + n2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -0.6666666667n + -1.777777778 + n2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -0.6666666667n + n2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -0.6666666667n + n2 = 0 + -1.777777778 -0.6666666667n + n2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -0.6666666667n + n2 = -1.777777778 The n term is -0.6666666667n. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667n + 0.1111111112 + n2 = -1.777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667n + n2 = -1.777777778 + 0.1111111112 Combine like terms: -1.777777778 + 0.1111111112 = -1.6666666668 0.1111111112 + -0.6666666667n + n2 = -1.6666666668 Factor a perfect square on the left side: (n + -0.3333333334)(n + -0.3333333334) = -1.6666666668 Can't calculate square root of the right side. The solution to this equation could not be determined.
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